html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.0954.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Sin[c z]^m Cosh[a z], z] == 2^(-1 - m) z^\[Alpha] ((Binomial[m, m/2] ((a z)^\[Alpha] Gamma[\[Alpha], (-a) z] + ((-a) z)^\[Alpha] Gamma[\[Alpha], a z]) (-1 + Mod[m, 2]))/ (((-a) z)^\[Alpha] (a z)^\[Alpha]) - Sum[((-1)^k Binomial[m, k] (((a + I c (2 k - m)) z)^\[Alpha] (((-a - 2 I c k + I c m) z)^\[Alpha] (((a + I c (-2 k + m)) z)^\[Alpha] Gamma[\[Alpha], (-a + 2 I c k - I c m) z] (Cos[(m Pi)/2] - I Sin[(m Pi)/2]) + ((-a + 2 I c k - I c m) z)^\[Alpha] Gamma[\[Alpha], (a + I c (-2 k + m)) z] (Cos[(m Pi)/2] + I Sin[(m Pi)/2])) + ((-a + 2 I c k - I c m) z)^\[Alpha] ((a + I c (-2 k + m)) z)^ \[Alpha] Gamma[\[Alpha], (-a - 2 I c k + I c m) z] (Cos[(m Pi)/2] + I Sin[(m Pi)/2])) + ((-a - I c (2 k - m)) z)^\[Alpha] ((-a + 2 I c k - I c m) z)^\[Alpha] ((a + I c (-2 k + m)) z)^\[Alpha] Gamma[\[Alpha], (a + I c (2 k - m)) z] (Cos[(m Pi)/2] - I Sin[(m Pi)/2])))/ (((-a - I c (2 k - m)) z)^\[Alpha] ((a + I c (2 k - m)) z)^\[Alpha] ((-a + 2 I c k - I c m) z)^\[Alpha] ((a + I c (-2 k + m)) z)^ \[Alpha]), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z α - 1 sin m ( c z ) cosh ( a z ) z 2 - m - 1 z α ( ( - a z ) - α ( a z ) - α ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( Γ ( α , a z ) ( - a z ) α + ( a z ) α Γ ( α , - a z ) ) ( m mod 2 \$CellContext`m 2 - 1 ) - k = 0 m - 1 2 ( - 1 ) k ( ( - a - c ( 2 k - m ) ) z ) - α ( ( a + c ( 2 k - m ) ) z ) - α ( ( - a + 2 c k - c m ) z ) - α ( ( a + c ( m - 2 k ) ) z ) - α ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( ( Γ ( α , ( a + c ( m - 2 k ) ) z ) ( cos ( m π 2 ) + sin ( m π 2 ) ) ( ( - a + 2 c k - c m ) z ) α + ( ( a + c ( m - 2 k ) ) z ) α Γ ( α , ( - a + 2 c k - c m ) z ) ( cos ( m π 2 ) - sin ( m π 2 ) ) ) ( ( - a - 2 c k + c m ) z ) α + ( ( - a + 2 c k - c m ) z ) α ( ( a + c ( m - 2 k ) ) z ) α Γ ( α , ( - a - 2 c k + c m ) z ) ( cos ( m π 2 ) + sin ( m π 2 ) ) ) ( ( a + c ( 2 k - m ) ) z ) α + ( ( - a - c ( 2 k - m ) ) z ) α ( ( - a + 2 c k - c m ) z ) α ( ( a + c ( m - 2 k ) ) z ) α Γ ( α , ( a + c ( 2 k - m ) ) z ) ( cos ( m π 2 ) - sin ( m π 2 ) ) ) ) /; m + Condition z z α -1 c z m a z 2 -1 m -1 z α -1 a z -1 α a z -1 α Binomial m m 2 -1 Gamma α a z -1 a z α a z α Gamma α -1 a z \$CellContext`m 2 -1 -1 k 0 m -1 2 -1 -1 k -1 a -1 c 2 k -1 m z -1 α a c 2 k -1 m z -1 α -1 a 2 c k -1 c m z -1 α a c m -1 2 k z -1 α Binomial m k Gamma α a c m -1 2 k z m 2 -1 m 2 -1 -1 a 2 c k -1 c m z α a c m -1 2 k z α Gamma α -1 a 2 c k -1 c m z m 2 -1 -1 m 2 -1 -1 a -1 2 c k c m z α -1 a 2 c k -1 c m z α a c m -1 2 k z α Gamma α -1 a -1 2 c k c m z m 2 -1 m 2 -1 a c 2 k -1 m z α -1 a -1 c 2 k -1 m z α -1 a 2 c k -1 c m z α a c m -1 2 k z α Gamma α a c 2 k -1 m z m 2 -1 -1 m 2 -1 m SuperPlus [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18